论文标题
涉及部分痕迹的新矩阵不等式
A new matrix inequality involving partial traces
论文作者
论文摘要
令$ a $为$ m \ times m $ $阳性半缩块矩阵，每个块为$ n $ -square。我们分别为第一部分和第二部分跟踪编写$ \ mathrm {tr} _1 $和$ \ mathrm {tr} _2 $。在本文中，我们证明了以下不等式\ [（\ mathrm {tr} a）i_ {mn} - （\ Mathrm {tr} _2 _2 a）\ otimes i_n \ ge \ ge \ ge \ pm \ bigl（i_m \ otimes（i_m \ otimes（i_m \ otime）安多的结果[ILAS会议（2014）]和林[Canad。数学。公牛。 59（2016）585--591]，但也可以被视为Choi的最新结果的补充[线性多线性代数66（2018）1619--1625]。此外，还包括一些新的部分轨迹不平等现象，即半半足型矩阵。
Let $A$ be an $m\times m$ positive semidefinite block matrix with each block being $n$-square. We write $\mathrm{tr}_1$ and $\mathrm{tr}_2$ for the first and second partial trace, respectively. In this paper, we prove the following inequality \[ (\mathrm{tr} A)I_{mn} - (\mathrm{tr}_2 A) \otimes I_n \ge \pm \bigl( I_m\otimes (\mathrm{tr}_1 A) -A\bigr).\] This inequality is not only a generalization of Ando's result [ILAS Conference (2014)] and Lin [Canad. Math. Bull. 59 (2016) 585--591], but it also could be regarded as a complement of a recent result of Choi [Linear Multilinear Algebra 66 (2018) 1619--1625]. Additionally, some new partial traces inequalities for positive semidefinite block matrices are also included.
